Math Problem Statement
A restaurant offers delivery for their pizzas. The total cost is a delivery fee added to the price of the pizzas. One customer pays $25 to have 2 pizzas delivered. Another customer pays $58 for 5 pizzas. How many pizzas are delivered to a customer who pays $80?
Solution
We can set up a system of equations to solve for the price of a pizza and the delivery fee.
Define Variables:
- Let be the price of one pizza.
- Let be the delivery fee.
Given Information:
- A customer pays $25 for 2 pizzas:
- Another customer pays $58 for 5 pizzas:
Solve for and :
Step 1: Subtract the first equation from the second:
Step 2: Solve for :
Substituting into the first equation:
Step 3: Find the Number of Pizzas for $80:
Using the equation:
Thus, a customer who pays $80 receives 7 pizzas.
Would you like more details or have any questions?
Related Questions:
- What would be the cost for 10 pizzas, including delivery?
- If the restaurant removes the delivery fee, how much would each customer pay per pizza?
- What if the delivery fee increased to $5? How would that affect the cost?
- Can you create a general formula for the cost of pizzas with a delivery fee?
- If a customer has $100, how many pizzas can they order?
Math Tip:
When solving systems of equations, elimination is a powerful method when the coefficients of one variable are the same or can be made the same.
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Math Problem Analysis
Mathematical Concepts
Algebra
Systems of Equations
Linear Equations
Formulas
2p + d = 25
5p + d = 58
xp + d = 80
Theorems
Elimination Method for Solving Systems of Equations
Suitable Grade Level
Grades 8-10
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